Well, however you cut it, £1500 for a gearbox is ****ing expensive, but yes, it would improve matters. With a suitable final drive you could finally give the car a semi-decent turn of speed AND motorway usability.
Nervous at speed is just a nature of front-wheel drive geometry at the back of a car. In front wheel drive cars, it's called bump steer. No different here, you've just got it at the back instead of the front. Eek there are things you can do to improve it, like spherical rod ends, nylon bushes, etc. but IMHO the simple nature of design means it'll never be perfect.
Hard top removal/fitting is just a matter of a few minutes, no worries. Soft top is similar but the actual fitting of it takes a little longer. Once it's fitted as an assembly, putting it up/down is very quick indeed.
As for the K, you've clearly made your mind up there, so fair enough - but in short, the 1.4/1.6's are nowhere near as problematic.
GTMOC used to be great, I'm sure they still are, there's a yahoo groups for them (groups.yahoo.com/gtmoc from memory; I should know, I'm a moderator!! Oops!). GTM themselves are a great bunch of guys too, very helpful, although the Coupe/Rossa have long since left the ranch and are now handled by other guys.
Alan Britton took on the Rossa models, and he's a great chap, long standing club member so knows what's relevant still.